When the engine is cold-started, a catalytic converter provided in an exhaust system of the engine is cold. Exhaust gases are emitted through the inactive catalytic converter. In order to avoid such a situation, rapid catalyst warming-up control for rapidly activating the catalytic converter at the start of the engine is proposed.
According to an example of the rapid catalyst warming-up control, the amount of intake air introduced into the engine is increased when the engine is in an idling state immediately after the start of the engine. The rotational speed of the engine is increased, thereby increasing the heat energy of exhaust gases generated by the engine. The increased rotational speed is feedback controlled. The feedback control manipulates ignition timing of the engine so that the rotational speed converges to a target rotational speed. As the ignition timing is more retarded, the rotational speed is more reduced. Conversely, as the ignition timing is more advanced, the rotational speed is more increased.
According to a conventional method, the above manipulation for the ignition timing is implemented with PI control. Specifically, a difference between the actual rotational speed of the engine and a target rotational speed is determined. A proportional gain and an integral gain are calculated based on the difference. Based on the proportional gain and the integral gain, a corrective quantity for the ignition timing is determined. The ignition timing corrected with the corrective quantity is applied to the engine.
In the Japanese Patent Application Unexamined Publication No. 2000-110657 assigned to the same assignee of the invention, the above manipulation for the ignition timing is implemented with sliding mode control. According to the sliding mode control, a rate of reduction of a difference between the actual rotational speed and the target rotational speed can be variably designated with a parameter.
Generally, it is desirable that the rotational speed control when the engine is in an idling state immediately after the start of the engine (hereinafter referred to as “idling rotational speed control”) satisfies several requirements. First, it is desirable that the idling rotational speed control has a quick response (convergence performance) with which the actual rotational speed quickly converges to the target rotational speed. If the quick response requirement is satisfied, the catalytic converter can be quickly activated while the engine is quickly made stable. Second, it is desirable that the accuracy of the control is high. If the accuracy of the control is high, low-frequency vibrations in the rotational speed are prevented when the ignition timing is retarded. Third, it is desirable that high-frequency vibrations are suppressed. If the high-frequency vibrations are suppressed, noise that may occur inside the vehicle can be suppressed.
According to the idling rotational speed control by the above PI control, variations in the rotational speed may be different depending on whether the ignition timing is retarded or advanced. The gains of the PI control need to be adapted to operating conditions of the engine. Therefore, it is difficult to cause the actual rotational speed to converge to the target rotational speed. It is also difficult to keep the accuracy of the control at high level.
The idling rotational speed control by the above sliding mode control may cause high-frequency vibrations. In an experiment in which the rotational speed in an idling state immediately after the start of the engine was controlled according to the above sliding mode control, frequency components of the vibrations that occurred between the engine and the interior of the vehicle were measured. FIG. 35 shows resonance points of the vibration and sound transfer system in the experiment. Higher frequency components shown in a circle 500 are not directly caused by the rotational speed of the engine. These higher frequency components are caused by resonance that has occurred in the vibration and sound transfer system. Such frequency components may cause vibrations to seats, display, etc. inside the vehicle, making vehicle occupants uncomfortable.
Thus, there is a need for idling rotational speed control that has a quick response and high accuracy and that does not cause vibrations to the interior of the vehicle when the catalytic converter is quickly warmed up at the start of the engine.
Furthermore, in the sliding mode control, a switching function is determined. By bringing the value of the switching function to zero, the actual rotational speed converges to the target rotational speed. However, depending on operating conditions of the engine, it may be difficult to hold the switching function at zero. If the switching function cannot be held at zero, the entire control system may become unstable.
Thus, there is another need for control that stably causes the output of an object of the control to converge to a target value even when the switching function cannot be held at zero.